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The Structural Binding Energy of Nuclides as a
Function of the Number of Alpha Particles and
the Excess Neutrons and Protons They Contain

A previous study established that the effects of one additional neutron or proton on the structural binding energy of a nuclide is a bent linear function of the number of alpha particle the nuclide could contain. The structural binding energy of a nuclide is its binding energy less the amount which would be accounted for if its neutrons and protons whenever possible formed alpha particles. The display of the relationship between the structural binding energies of nuclides which could be made up entirely of alpha particles and the number of alpha particles is shown below along with the same relationship for such nuclides with only one extra neutron.

These bent line shapes are evidence of a shell structure. The bend points correspond to the magic numbers for neutrons and protons. The difference between the two is the effect of one neutron on the structural binding energies of the nuclides. The difference also has a bent line shape, as shown below.

A similar bent line form exists for the effect of one extra proton.

The purpose of this webpage is to report on the application of the above results to the set of all 2932 nuclides. The regression equation applied to all 2931 nuclides has a coefficient of determination (R²) of 0.9947. This means that 99.47 percent of the variation in structural binding energies is explained by the variations in the number of alpha particles and number of excess neutrons and protons. The bend points at 3, 7, 14, 25, 41 alpha particles, which correspond to nucleonic magic numbers of 6, 14, 28, 50 and 82. Also included are two variable to account for the effects of the formation of neutron pairs and proton pairs. Altogether there are 16 explanatory variables, the maximum number allowed by the EXCEL spread sheet used for the analysis. Thirteen of the sixteen regression coefficients are significantly different from zero at the 95 percent level of confidence.

For 1 to 3 alpha particles the increase in structural binding energy is 7.37 MeV per additional alpha particle. From 3 to 7 it is 9.95 MeV. From 7 to 14 it is 6.00 MeV. From 14 to 25 it is 4.90 MeV. Beyond 25 this value turns negative. From 25 to 41 it is −0.51 MeV and beyond 41 it is −6.61 MeV.

(To be continued.)

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